A Mineral X-ray Linear Attenuation Coefficient Tool (MXLAC ...

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A Mineral X-ray Linear Attenuation Coefficient Tool(MXLAC) to Assess Mineralogical Differentiation forX-ray Computed Tomography Scanning

Lunga C. Bam 1,2,*, Jodie A. Miller 1 and Megan Becker 3

1 Department of Earth Sciences, Stellenbosch University, Private Bag X1, Matieland 7601, South Africa;[email protected]

2 Department of Radiation Science, South African Nuclear Energy Corporation (Necsa),Pretoria 0001, South Africa

3 Centre for Minerals Research, Department of Chemical Engineering, University of Cape Town, Private Bag,Rondebosch 7701, South Africa; [email protected]

* Correspondence: [email protected]

Received: 9 April 2020; Accepted: 5 May 2020; Published: 15 May 2020�����������������

Abstract: X-ray computed tomography (XCT) is becoming one of the most important techniques inthe geosciences. The technique relies on linear attenuation coefficient differences in order to reveal theinternal structure of the rocks. In this work, we present a new excel macro tool, called MXLAC, which isa data bank with an excel interface that uses density, X-ray energy and the mineral chemical formulato allow users to calculate mineral linear attenuation coefficients that can then be used to determinediscrimination between mineral pairs. Elements within a mineral and specified by the chemicalformula, determine how the X-ray beam is attenuated. Analysis of a variety of scanned mineral pairswith similar densities and attenuation coefficients indicates that an attenuation coefficient differenceof greater than or equal to 6% at 45.5 keV effective X-ray energy is required for effective discriminationbetween two minerals using XCT with single energy scanning. This means that mineral pairs, such asquartz and pyrophyllite cannot be discriminated using the current XCT instruments due to the factthat the attenuation coefficient difference is less than 1.9% at 45.5 keV effective X-ray energy. Garnetsand a variety of other minerals were used as examples to illustrate the importance of knowingthe actual chemical formula of the mineral to demonstrate whether they can be partially or fullydiscriminated from each other.

Keywords: X-ray computed tomography; linear attenuation coefficient; minerals; effectiveX-ray energy

1. Introduction

X-ray computed tomography (XCT) is a non-destructive technique that utilizes X-rays to imagethe 3D internal structure of a wide variety of materials [1–3]. Soon after its development in the medicalsciences in the 1970s [4], it attracted considerable attention within the geosciences due to its potentialto visualise the internal structure of rocks and minerals [5–7]. In particular, the ability of the techniqueto determine the mineral content, distribution of minerals, mineral texture, porosity and pore structurenetwork, at a variety of scales, made it an attractive technique across diverse fields from petrologyto palaeontology to minerals processing [2,8–11]. Micro and nano XCT has also been used widely tocharacterize shale gas pore framework [12–14]. XCT has proven to be an important analytical techniquefor the analysis of drill cores, that lend themselves to analysis because of their uniform sample geometry.Material density [15,16] as well as ore grade [17] have been successfully calculated from drill core usingadvanced segmentation methods. More recently, it has been proposed to combine XCT with grey level

Minerals 2020, 10, 441; doi:10.3390/min10050441 www.mdpi.com/journal/minerals

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co-occurrence matrices (GLCM) to generate algorithms that will automatically interrogate texture in3D applications using drill core [18].

XCT images record the difference in density by means of grey values that represent the linearattenuation coefficient of each and every mineral present within the specimen [2,7]. The interaction ofX-rays with minerals depends not only on the mineral density (a function of mineral chemistry andatomic structure) but also on the thickness (grain size) and effective atomic number of the mineral.This means that if the density variation between the minerals present is large, the X-ray beam isattenuated differently, resulting in distinct grey values. This makes the XCT technique attractive todifferent material science disciplines. However, if the density difference between minerals is small,then it is difficult for XCT to differentiate them because of similar attenuation response of the mineralsresulting in similar grey values [2]. Because of this, different combinations of minerals or mineralassemblages are more amenable to interrogation by XCT than others. In particular, some combinationsof minerals or mineral pairs cannot be differentiated from one another because of the similarity inattenuation response. In such cases, it is important to know up front, the limitations of the XCT systemwith respect to the mineral assemblage or problem being worked with.

In this contribution, a simple way to evaluate whether different minerals can be differentiated,on the basis of their linear attenuation coefficient, is presented as the downloadable mineral X-raylinear attenuation coefficient (MXLAC) file. MXLAC represents an attenuation coefficient ‘databank’, developed in the form of a user-friendly excel spreadsheet that uses macros to calculate linearattenuation coefficients at any effective energy (with any increment of choice) between 41.7 and 72.6 keVwhich is equivalent to an X-ray energy spectrum of between 60 and 225 keV. The conversion of theX-ray energy spectrum to an effective energy that is correlated to the X-ray voltage, is important forXCT users because it allows an accurate calculation of the linear attenuation coefficient for differentminerals. An application of MXLAC is demonstrated by looking at several examples including highdensity iron-ore minerals, some of which cannot be differentiated by XCT.

2. Methodology

The development of the MXLAC data bank involved several steps. The first step was to collectdifferent energy spectrums of a tungsten target under a high voltage (kV) and convert them into effectiveenergies equivalent to a monochromatic beam of the X-ray energy spectrum. This allows evaluation ofhow mineralogical grey value information is affected by scanning parameters, different filter materials,sample size and beam hardening by comparing the effective linear attenuation difference with themeasured grey value difference. Tungsten is normally used as the target in XCT instruments becauseit has high flux and can withstand high temperatures. The second step was to collect the NationalInstitute of Standards and Technology (NIST) database for attenuation and energy information for allelements from 41.7 to 72.6 keV and compile this information into an excel spreadsheet. The collectedNIST database consists of predetermined energy and linear attenuation coefficient information whichprohibit the calculation of linear attenuation coefficient for any X-ray energy increment. To deal withthis, different interpolation functions have been incorporated into the spreadsheet in order to calculatelinear attenuation coefficient for any X-ray energy. The third step was to develop the excel macros thattake the compiled NIST elemental data and convert it to linear attenuation coefficients for any mineral.

2.1. Tungsten Energy Spectrum

Different energy spectrums of a tungsten target under a high voltage (kV) were collected using agermanium detector (Figure 1). Although the X-ray system being used to collect the energy spectrumscan reach high X-ray voltage of 225 kV, this level of voltage affects mineralogical discrimination dueto smaller linear attenuation coefficient difference. The set voltage on the target is equivalent to themaximum energy of the produced spectrum. The spectrum consists of different proportions of variousenergies because of the polychromatic nature of the X-ray beam. The varying energy proportions eachinteract differently with minerals, thus making the associated linear attenuation coefficient calculations

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complex—minerals absorb more energy at the lower energy range compared to the higher energyrange of the spectrum. To simplify the interpretation of the interaction of the X-ray spectrum with amineral, an effective energy of the spectrum was calculated. An effective energy is a weighted averageof an actual polychromatic beam. Although previously the effective energy has been assumed to beclose to 30–40% of the peak energy [19], it is more accurate to calculate it for each spectrum.

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attenuation coefficient calculations complex—minerals absorb more energy at the lower energy range compared to the higher energy range of the spectrum. To simplify the interpretation of the interaction of the X-ray spectrum with a mineral, an effective energy of the spectrum was calculated. An effective energy is a weighted average of an actual polychromatic beam. Although previously the effective energy has been assumed to be close to 30–40% of the peak energy [19], it is more accurate to calculate it for each spectrum.

Figure 1. Different tungsten energy spectrums collected at different X-energies [20].

One way to determine the effective energy is to use the aluminium half-value layer method [21–23]. To do this, the effective energy is calculated by converting the X-ray energy spectrum from polychromatic to monochromatic (Figure 2). This is done by combining all the photon energies (E) of the spectrum, relative to the count ratio for each photon energy of the spectrum, using Equations (1 and 2). Equation (1) combines all the counts with respect to each energy of the spectrum. Calculating the effective energy using Equations (1 and 2) is more reliable as compared to calculating it using the mean equation. The mean equation does not take into consideration the counts for each energy photon of the spectrum. The resultant effective energies (Figure 2) calculated using Equation (2) are similar to the ones reported by Yada et al. [23] using the same method. = + +. . . + (1) Effective energy = × + × +. . . + × (2)

Conversion of the spectrum into a single energy simplifies the linear attenuation coefficient calculations. In addition to this, it allows a direct comparison of theoretically calculated linear attenuation coefficients with the experimental ones. This means that the calculated linear attenuation coefficients can be used to predict how minerals will correlate with grey values on radiographs or 2D image slices taken from 3D image volumes. Grey values are a direct representation of the average linear attenuation coefficients of minerals [24,25]. Where samples are high density or larger volume, it can be difficult to calculate accurate linear attenuation coefficients since the X-ray beam is hardened as it passes through the sample [26] causing the effective energy to be higher [27]. This will affect the expected discrimination between the mineralogical information based on the initially calculated linear attenuation coefficients. Therefore, in such a case, a step-wise protocol should be used to determine what is affecting the discrimination between the minerals.

Figure 1. Different tungsten energy spectrums collected at different X-energies [20].

One way to determine the effective energy is to use the aluminium half-value layer method [21–23].To do this, the effective energy is calculated by converting the X-ray energy spectrum from polychromaticto monochromatic (Figure 2). This is done by combining all the photon energies (E) of the spectrum,relative to the count ratio for each photon energy of the spectrum, using Equations (1) and (2).Equation (1) combines all the counts with respect to each energy of the spectrum. Calculating theeffective energy using Equations (1) and (2) is more reliable as compared to calculating it using themean equation. The mean equation does not take into consideration the counts for each energy photonof the spectrum. The resultant effective energies (Figure 2) calculated using Equation (2) are similar tothe ones reported by Yada et al. [23] using the same method.

CountTotal = Count1(E1) + Count2(E2) + . . .+ Countn(En) (1)

Effective energy (keV) =

[Count1(E1)

CountTotal

]× E1 +

[Count2(E2)

CountTotal

]× E2 + . . .+

[Countn(En)

CountTotal

]× E2 (2)

Conversion of the spectrum into a single energy simplifies the linear attenuation coefficientcalculations. In addition to this, it allows a direct comparison of theoretically calculated linearattenuation coefficients with the experimental ones. This means that the calculated linear attenuationcoefficients can be used to predict how minerals will correlate with grey values on radiographs or 2Dimage slices taken from 3D image volumes. Grey values are a direct representation of the averagelinear attenuation coefficients of minerals [24,25]. Where samples are high density or larger volume,it can be difficult to calculate accurate linear attenuation coefficients since the X-ray beam is hardenedas it passes through the sample [26] causing the effective energy to be higher [27]. This will affect theexpected discrimination between the mineralogical information based on the initially calculated linearattenuation coefficients. Therefore, in such a case, a step-wise protocol should be used to determinewhat is affecting the discrimination between the minerals.

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Figure 2. Correlation between the effective X-ray energy and the X-ray energy spectrum of the tungsten target [20].

2.2. Development of the Attenuation Coefficient Data Bank

The mass attenuation coefficient data from NIST represent the mass attenuation coefficients for all elements at different X-ray energies (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html). In order to properly utilise the mass attenuation coefficient data for discrete X-ray energies or X-ray energies similar to the collected spectrums mentioned above, a set of linear and polynomial equations (Equations (3–5)) were fitted to represent the change of mass attenuation coefficient as the X-ray energy increases (Figure 3). Iron has been used as an example to illustrate the decreasing mass attenuation coefficient with increasing X-ray energy and the spike in mass attenuation coefficient at 7.112 keV is due to a K-edge absorption. These equations were fitted for all elements in the periodic table taking into consideration the behaviour of mass attenuation coefficients with respect to energy. Fitting different equations was done to minimise deviations between the expected mass attenuation coefficients with the calculated ones. = mx + c (3) = a + + (4) = a + + + + + (5)

The x and y-axis represents the X-ray energy and mass attenuation coefficient respectively. This method was repeated for all the elements. In cases where Equations (3 and 4) could not provide satisfactory mass attenuation coefficients, Equation (5) (high order polynomial) was used to minimize deviations between the mass attenuation coefficient calculated in this spreadsheet and that provided by NIST. The mass attenuation coefficient for minerals, µ/ρ (cm2/g), was calculated using Equation (6) where ωi is the weight fraction of ith element [24,25]. The linear attenuation coefficient, µ (cm−1), was then obtained by rearranging Equation (6) to give Equation (7).

Figure 2. Correlation between the effective X-ray energy and the X-ray energy spectrum of the tungstentarget [20].

2.2. Development of the Attenuation Coefficient Data Bank

The mass attenuation coefficient data from NIST represent the mass attenuation coefficients for allelements at different X-ray energies (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html).In order to properly utilise the mass attenuation coefficient data for discrete X-ray energies or X-rayenergies similar to the collected spectrums mentioned above, a set of linear and polynomial equations(Equations (3)–(5)) were fitted to represent the change of mass attenuation coefficient as the X-rayenergy increases (Figure 3). Iron has been used as an example to illustrate the decreasing massattenuation coefficient with increasing X-ray energy and the spike in mass attenuation coefficient at7.112 keV is due to a K-edge absorption. These equations were fitted for all elements in the periodictable taking into consideration the behaviour of mass attenuation coefficients with respect to energy.Fitting different equations was done to minimise deviations between the expected mass attenuationcoefficients with the calculated ones.

y = mx + c (3)

y = ax2 + bx + c (4)

y = ax5 + bx4 + cx3 + dx2 + ex + f (5)

The x and y-axis represents the X-ray energy and mass attenuation coefficient respectively.This method was repeated for all the elements. In cases where Equations (3) and (4) could not providesatisfactory mass attenuation coefficients, Equation (5) (high order polynomial) was used to minimizedeviations between the mass attenuation coefficient calculated in this spreadsheet and that providedby NIST. The mass attenuation coefficient for minerals, µ/ρ (cm2/g), was calculated using Equation (6)where ωi is the weight fraction of ith element [24,25]. The linear attenuation coefficient, µ (cm−1),was then obtained by rearranging Equation (6) to give Equation (7).

µ

ρ= Σi

(µ

ρ

)i×ωi (6)

µ =

[Σi

(µ

ρ

)i×ωi

]ρ (7)

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Figure 3. The representation of iron mass attenuation coefficient by different equations (linear, second and fifth order polynomial). The black lines represent linear equations (Equation (1)) and the red and green curves represent the second and fifth order polynomial equations (Equations (2 and 3)).

= ∑ × (6)

= ∑ × (7)

2.3. Development of User Spreadsheet

The MXLAC spreadsheet (also provided as supplementary materials) calculates the linear attenuation coefficient as an output using Equation (7). The spreadsheet is designed to be user-friendly with minimal inputs required to immediately calculate the linear attenuation coefficient for any mineral and can accommodate complex mineral compositions. Calculating the linear attenuation coefficient of different minerals requires a user to insert the actual number of elements (both cations and anions) present within a mineral (i.e., the exact mineral composition), the mineral density and the relevant effective energy under the appropriate columns (Figure 4). MXLAC can calculate the linear attenuation coefficient of the same or different mineral at two different energies simultaneously. This allows a direct comparison of the linear attenuation coefficient of minerals to better understand the impact of grey value variation on image slices in order to optimize mineralogical discrimination prior to scanning. The voltage is equivalent to the energy spectrum indicated in the column for the tungsten spectrum. The effective energy is converted from the tungsten spectrum and is utilized to calculate the linear attenuation coefficient as an output under the X-ray attenuation coefficient cell.

2.4. Validation of Linear Attenuation Coefficients

To validate the ability of MXLAC to predict mineral discrimination using linear attenuation coefficients, thirteen minerals were scanned using a micro-focus X-ray computed tomography

Figure 3. The representation of iron mass attenuation coefficient by different equations (linear, secondand fifth order polynomial). The black lines represent linear equations (Equation (1)) and the red andgreen curves represent the second and fifth order polynomial equations (Equations (2) and (3)).

2.3. Development of User Spreadsheet

The MXLAC spreadsheet (also provided as Supplementary Materials) calculates the linearattenuation coefficient as an output using Equation (7). The spreadsheet is designed to be user-friendlywith minimal inputs required to immediately calculate the linear attenuation coefficient for any mineraland can accommodate complex mineral compositions. Calculating the linear attenuation coefficient ofdifferent minerals requires a user to insert the actual number of elements (both cations and anions)present within a mineral (i.e., the exact mineral composition), the mineral density and the relevanteffective energy under the appropriate columns (Figure 4). MXLAC can calculate the linear attenuationcoefficient of the same or different mineral at two different energies simultaneously. This allows a directcomparison of the linear attenuation coefficient of minerals to better understand the impact of greyvalue variation on image slices in order to optimize mineralogical discrimination prior to scanning.The voltage is equivalent to the energy spectrum indicated in the column for the tungsten spectrum.The effective energy is converted from the tungsten spectrum and is utilized to calculate the linearattenuation coefficient as an output under the X-ray attenuation coefficient cell.

2.4. Validation of Linear Attenuation Coefficients

To validate the ability of MXLAC to predict mineral discrimination using linear attenuationcoefficients, thirteen minerals were scanned using a micro-focus X-ray computed tomography system(Nikon XTH 225 ST) and their grey values compared. Prior to scanning, the minerals were groupedas follows based on linear attenuation coefficient and mineral density: (a) almandine, andraditeand grossular; (b) quartz, kaolinite, dolomite, calcite; (c) fluorite, apatite; and (d) goethite, chromite,magnetite and hematite. The density information for all the minerals was obtained from https://www.mindat.org. All the minerals were scanned at 70 kV (45.5 keV effective energy) using differentfilter materials as well as having no filter (Table 1). The set voltage on the target represents thecollected energy spectrum with a maximum energy of 70 keV. The samples were scanned at a 20 µmresolution with 3000 projections and 4 s exposure time. The selection of a high number of projectionsand high exposure time optimises mineralogical discrimination using grey values and minimisesimage noise associated with a low number of projections and low exposure time. The scanned

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data were reconstructed using CT Pro 3D software version 3.1.9 by applying various built-in beamhardening correction factors within the software. The mean grey value analysis was conducted inall the samples using VG Studio Max version 3.2 software to determine the required grey valuedifference that renders minerals to be discriminated. Before the grey value analysis was conducted,the region growing tool was used to remove background information from all the minerals in orderto deal only with the mineral grey values themselves. It was important to define the mineral greyvalue range because it was used to assign a false colour to the individual minerals in order todetermine how grey values of different minerals overlap with each other. The mineral identities,compositions, as well as compositional homogeneity were confirmed using both standardized scanningelectron microscopy (SEM) and quantitative evaluation of materials by scanning electron microscopy(QEMSCAN). Individual minerals were prepared into polished sections and characterised using anFEI QEMSCAN 650F instrument on the field image analysis routine at the University of Cape Town.Measurements were run at 25 kV, 10 nA using a 100 micron pixel spacing. The same sections were thenused for SEM-EDS analysis conducted at the Electron Microscopy Unit of the Central Analytical Facility(Stellenbosch University, South Africa) using Zeiss EVO MA15VP Scanning Electron Microscope.The measurements were run at between 20 kV to 30 kV, with a working distance for EDS analysesof 8.5 mm and magnifications ranging between 1000× and 5000×. Appropriate ASTIMEX© certifiedmineral standards were used for different element concentrations even within similar mineral families,such as garnet (e.g., almandine, andradite and grossular). The validation process also providedinformation about possible inclusions that may: (a) affect expected discrimination between mineralsand (b) provide a false assumption that a mineral can be discriminated from another mineral dueto the presence of non-uniformly distributed inclusions that cannot be easily detected by the XCTscanning resolution.

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Figure 4. Illustration of the MXLAC user interface for calculation of mineral linear attenuation coefficients, with inputs under number of atoms in the compound, density and voltage for each mineral indicated in blue. The calculated output is show in green.

Table 1. Scanning parameters to optimize discrimination between minerals.

Exposure Time (sec) No. of Projections Voltage (kV)/

Effective Energy (keV) Filter Material

4 3000 70/45.5 No filter 4 3000 70/45.5 0.25 mm Cu 4 3000 70/45.5 1mm Al + 1mm Cu

3. Results

Here we present the results of this study in two parts. In the first part, we use MXLAC to calculate linear attenuation coefficients for a variety of minerals of varying compositional complexity using the compiled spreadsheet. These values are compared to those that can be generated using the NIST database to assess the accuracy of the MXLAC spreadsheet. Thereafter, mineral linear attenuation coefficients, calculated using MXLAC, are compared with the mineral grey values, generated using XCT, to evaluate the minimum difference in attenuation coefficient needed to be able to discriminate two minerals using XCT.

3.1. Calculated Linear Attenuation Coefficients

Table 2 lists a wide range of minerals (40 in total) with different densities and chemical compositions. The 40 minerals were picked to evaluate different mineral compositional complexity in terms of both the range of elements present in the mineral as well as the mineral structure. It includes minerals regarded as ore minerals (e.g., chalcopyrite, hematite and sphalerite), clay minerals (e.g., kaolinite), carbonates (e.g., calcite and dolomite) and end-member varieties of the same mineral (e.g., pyrope, almandine, grossular, andradite and spessartine garnets). The maximum % error difference between the calculated linear attenuation coefficients using MXLAC and those

Figure 4. Illustration of the MXLAC user interface for calculation of mineral linear attenuationcoefficients, with inputs under number of atoms in the compound, density and voltage for each mineralindicated in blue. The calculated output is show in green.

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Table 1. Scanning parameters to optimize discrimination between minerals.

Exposure Time (sec) No. of Projections Voltage (kV)/Effective Energy (keV) Filter Material

4 3000 70/45.5 No filter4 3000 70/45.5 0.25 mm Cu4 3000 70/45.5 1 mm Al + 1 mm Cu

3. Results

Here we present the results of this study in two parts. In the first part, we use MXLAC to calculatelinear attenuation coefficients for a variety of minerals of varying compositional complexity usingthe compiled spreadsheet. These values are compared to those that can be generated using the NISTdatabase to assess the accuracy of the MXLAC spreadsheet. Thereafter, mineral linear attenuationcoefficients, calculated using MXLAC, are compared with the mineral grey values, generated usingXCT, to evaluate the minimum difference in attenuation coefficient needed to be able to discriminatetwo minerals using XCT.

3.1. Calculated Linear Attenuation Coefficients

Table 2 lists a wide range of minerals (40 in total) with different densities and chemical compositions.The 40 minerals were picked to evaluate different mineral compositional complexity in terms of boththe range of elements present in the mineral as well as the mineral structure. It includes mineralsregarded as ore minerals (e.g., chalcopyrite, hematite and sphalerite), clay minerals (e.g., kaolinite),carbonates (e.g., calcite and dolomite) and end-member varieties of the same mineral (e.g., pyrope,almandine, grossular, andradite and spessartine garnets). The maximum % error difference betweenthe calculated linear attenuation coefficients using MXLAC and those given by the NIST database,is 4.96% at 44.79 keV and 4.81% at 62.53 keV. At 44.79 keV, nine minerals have a % error less than 2%,whilst at 62.53 keV, 22 minerals have a % error less than 2% (Table 2). The X-ray energy of 44.79 keV and62.53 keV from the NIST database were selected as they are sufficiently close enough to the calculatedeffective energy of the energy spectrums collected at the voltage of 70 kV and 140 kV respectively.This provides more information about the expected % error at both 70 kV and 140 kV. The calculatedmineral linear attenuation coefficients increase with increasing density, but the trend is not linearand the mineral attenuation is lower at 62.53 keV as expected (Figure 5). Interrogation of the dataindicates that it is not possible to predict the linear attenuation coefficient based on mineral densityalone. Comparison of sphalerite and corundum for example, shows similar densities (4.1 g/cm3 and4.02 g/cm3 respectively) but large differences in linear attenuation coefficient (11.9 cm−1 and 1.34 cm−1,respectively). Because the minerals have similar densities, the logical assumption would be that theseminerals cannot be differentiated using XCT, which would be incorrect, based on the difference in theirlinear attenuation coefficients.

In contrast, dolomite and corundum have similar attenuation coefficients (1.33 cm−1 and 1.34 cm−1

respectively) suggesting they cannot be differentiated using XCT, but these two minerals have significantdifferences in density (2.85 g/cm3 and 4.02 g/cm3 respectively). In this case, the difference in densitywould suggest these minerals can be differentiated using XCT, which is not true, based on the linearattenuation coefficient information. The above examples illustrate the complexity of trying to evaluatewhether XCT is useful for different mineral pairs, although the likelihood of dolomite and corundumnaturally occurring in the same rock is low. A more likely combination is dolomite and calcite. In thiscase, the density of calcite is 2.71 g/cm3 in comparison to the 2.85 g/cm3 of dolomite and the linearattenuation of calcite is 1.73 cm−1 in comparison to the 1.33 cm−1 of dolomite. In this example, it isunclear if these differences are large enough to be able to differentiate these minerals using XCT.Therefore, the second part of the results presented here, uses MXLAC to evaluate the minimumdifference in linear attenuation coefficient needed to differentiate two minerals.

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given by the NIST database, is 4.96% at 44.79 keV and 4.81% at 62.53 keV. At 44.79 keV, nine minerals have a % error less than 2%, whilst at 62.53 keV, 22 minerals have a % error less than 2% (Table 2). The X-ray energy of 44.79 keV and 62.53 keV from the NIST database were selected as theyare sufficiently close enough to the calculated effective energy of the energy spectrums collected atthe voltage of 70 kV and 140 kV respectively. This provides more information about the expected % error at both 70 kV and 140 kV. The calculated mineral linear attenuation coefficients increase withincreasing density, but the trend is not linear and the mineral attenuation is lower at 62.53 keV as expected (Figure 5). Interrogation of the data indicates that it is not possible to predict the linearattenuation coefficient based on mineral density alone. Comparison of sphalerite and corundum forexample, shows similar densities (4.1 g/cm3 and 4.02 g/cm3 respectively) but large differences in linear attenuation coefficient (11.9 cm−1 and 1.34 cm−1, respectively). Because the minerals havesimilar densities, the logical assumption would be that these minerals cannot be differentiated using XCT, which would be incorrect, based on the difference in their linear attenuation coefficients.

In contrast, dolomite and corundum have similar attenuation coefficients (1.33 cm−1 and 1.34 cm−1 respectively) suggesting they cannot be differentiated using XCT, but these two minerals have significant differences in density (2.85 g/cm3 and 4.02 g/cm3 respectively). In this case, the difference in density would suggest these minerals can be differentiated using XCT, which is not true, based on the linear attenuation coefficient information. The above examples illustrate the complexity of trying to evaluate whether XCT is useful for different mineral pairs, although the likelihood of dolomiteand corundum naturally occurring in the same rock is low. A more likely combination is dolomiteand calcite. In this case, the density of calcite is 2.71 g/cm3 in comparison to the 2.85 g/cm3 of dolomite and the linear attenuation of calcite is 1.73 cm−1 in comparison to the 1.33 cm−1 of dolomite. In this example, it is unclear if these differences are large enough to be able to differentiate these minerals using XCT. Therefore, the second part of the results presented here, uses MXLAC to evaluate the minimum difference in linear attenuation coefficient needed to differentiate two minerals.

A B

Figure 5. Variation of linear attenuation coefficients for different mineral densities calculated with MXLAC and NIST at: A) 44.79 keV and B) 62.53 keV X-ray energy.

3.2. Minimum Attenuation Coefficient Difference to Determine Discrimination

XCT, SEM-EDS and QEMSCAN analysis was undertaken on 13 minerals from Table 2 which provided data that could be properly interrogated for grey level variation (Figure 6 and Table 3). Table 4 shows comparison of different mineral pairs from these 13 minerals. The pairs are based on minerals occurring in the same QEMSCAN polished mount so that the grey values are comparable and reflect the linear attenuation coefficient (Figure 6). Minerals with a linear attenuation coefficient

Figure 5. Variation of linear attenuation coefficients for different mineral densities calculated withMXLAC and NIST at: (A) 44.79 keV and (B) 62.53 keV X-ray energy.

3.2. Minimum Attenuation Coefficient Difference to Determine Discrimination

XCT, SEM-EDS and QEMSCAN analysis was undertaken on 13 minerals from Table 2 whichprovided data that could be properly interrogated for grey level variation (Figure 6 and Table 3). Table 4shows comparison of different mineral pairs from these 13 minerals. The pairs are based on mineralsoccurring in the same QEMSCAN polished mount so that the grey values are comparable and reflect thelinear attenuation coefficient (Figure 6). Minerals with a linear attenuation coefficient less than 2 cm−1

did not require the utilisation of any filters to optimize grey value variation. This is demonstrated byquartz, kaolinite, dolomite and calcite (Figure 6D–G) respectively). However, minerals with a linearattenuation coefficient more than 3 cm−1 required application of a filter in order to optimise X-raypenetration and minimise beam hardening. In the case of magnetite and hematite (Figure 6L,M),the highest density minerals examined, a combination of filter materials and high beam hardeningcorrection factor was used to minimise the impact of beam hardening.

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hematite (Figure 6L and M), the highest density minerals examined, a combination of filter materials and high beam hardening correction factor was used to minimise the impact of beam hardening.

Figure 6. Grey value variation of different minerals with their corresponding false colour to illustrate discrimination between minerals at 45.5 keV effective energy: (A) almandine, (B) andradite, (C) grossular, (D) quartz, (E) kaolinite, (F) dolomite, (G) calcite, (H) apatite, (I) fluorite, (J) goethite, (K) chromite, (L) magnetite and (M) hematite.

Table 2. Comparison of the NIST and MXLAC attenuation coefficients for different types of minerals.

Mineral. Chemical Formula Density (g/cm3)

NIST MXLAC

%Error

NIST MXLAC

%Error Attenuation Coefficient

(cm−1), at 44.79 keV

Attenuation Coefficient

(cm−1), at 62.53 k3V

Acanthite Ag2S 7.24 79.68 80.60 1.14 32.43 32.70 0.83 Almandine Fe3Al2Si3O12 4.32 4.77 4.55 4.56 2.21 2.19 0.53 Andradite Ca3Fe3+2Si3O12 3.86 4.09 3.91 4.44 1.91 1.90 0.35 Ankerite CaFe(CO3)2 3.20 3.33 3.19 4.20 1.56 1.56 0.00 Apatite Ca5(PO4)3OH 3.19 2.36 2.28 3.39 1.19 1.19 0.00

Arsenopyrite FeAsS 6.18 20.23 20.40 0.83 8.26 8.51 2.94 Barite BaSO4 4.48 48.67 48.10 1.17 20.31 21.00 3.29 Borax Na2B4O5(OH)4·8H2O 1.70 0.42 0.41 3.02 0.34 0.33 2.94 Calcite CaCO3 2.71 1.80 1.73 4.09 0.94 0.94 0.54

Carnotite K2(UO2)2(VO4)2·3H2O 4.91 38.90 40.60 4.19 17.83 17.20 3.53 Chalcocite Cu2S 5.60 16.48 17.20 4.19 6.72 6.49 3.42

Chalcopyrite CuFeS2 4.20 9.48 9.58 1.04 3.95 3.89 1.52 Chlorite (Mg)5Al2Si3O10(OH)8 3.20 1.09 1.04 4.44 0.73 0.72 1.30

Chromite FeCr2O4 4.79 7.93 8.03 1.21 3.42 3.40 0.55 Corundum Al2O3 4.02 1.41 1.34 4.96 0.92 0.91 1.09 Dolomite CaMg(CO3)2 2.85 1.39 1.33 4.32 0.80 0.80 0.00 Fluorite CaF2 3.13 2.50 2.41 3.76 1.23 1.23 0.38 Gibbsite Al(OH)3 2.34 0.74 0.70 4.89 0.52 0.51 2.16 Goethite FeO(OH) 4.28 7.34 7.01 4.49 3.17 3.16 0.22

Grossular Ca3Al2Si3O12 3.65 2.22 2.12 4.45 1.19 1.18 0.77 Hematite Fe2O3 5.26 9.89 9.45 4.48 4.21 4.20 0.16 Ilmenite FeTiO3 4.76 7.26 6.95 4.34 3.17 3.13 1.05 Kaolinite Al2Si2O5(OH)4 2.60 0.91 0.87 4.90 0.60 0.59 1.95

K-feldspar KAlSi3O8 2.56 1.22 1.16 4.65 0.71 0.71 0.00

Figure 6. Grey value variation of different minerals with their corresponding false colour to illustratediscrimination between minerals at 45.5 keV effective energy: (A) almandine, (B) andradite, (C) grossular,(D) quartz, (E) kaolinite, (F) dolomite, (G) calcite, (H) apatite, (I) fluorite, (J) goethite, (K) chromite,(L) magnetite and (M) hematite.

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Table 2. Comparison of the NIST and MXLAC attenuation coefficients for different types of minerals.

Mineral. Chemical FormulaDensity(g/cm3)

NIST MXLAC

%Error

NIST MXLAC

%ErrorAttenuationCoefficient (cm−1),

at 44.79 keV

AttenuationCoefficient (cm−1),

at 62.53 keV

Acanthite Ag2S 7.24 79.68 80.60 1.14 32.43 32.70 0.83Almandine Fe3Al2Si3O12 4.32 4.77 4.55 4.56 2.21 2.19 0.53Andradite Ca3Fe3+

2Si3O12 3.86 4.09 3.91 4.44 1.91 1.90 0.35Ankerite CaFe(CO3)2 3.20 3.33 3.19 4.20 1.56 1.56 0.00Apatite Ca5(PO4)3OH 3.19 2.36 2.28 3.39 1.19 1.19 0.00

Arsenopyrite FeAsS 6.18 20.23 20.40 0.83 8.26 8.51 2.94Barite BaSO4 4.48 48.67 48.10 1.17 20.31 21.00 3.29Borax Na2B4O5(OH)4·8H2O 1.70 0.42 0.41 3.02 0.34 0.33 2.94Calcite CaCO3 2.71 1.80 1.73 4.09 0.94 0.94 0.54

Carnotite K2(UO2)2(VO4)2·3H2O 4.91 38.90 40.60 4.19 17.83 17.20 3.53Chalcocite Cu2S 5.60 16.48 17.20 4.19 6.72 6.49 3.42

Chalcopyrite CuFeS2 4.20 9.48 9.58 1.04 3.95 3.89 1.52Chlorite (Mg)5Al2Si3O10(OH)8 3.20 1.09 1.04 4.44 0.73 0.72 1.30

Chromite FeCr2O4 4.79 7.93 8.03 1.21 3.42 3.40 0.55Corundum Al2O3 4.02 1.41 1.34 4.96 0.92 0.91 1.09Dolomite CaMg(CO3)2 2.85 1.39 1.33 4.32 0.80 0.80 0.00Fluorite CaF2 3.13 2.50 2.41 3.76 1.23 1.23 0.38Gibbsite Al(OH)3 2.34 0.74 0.70 4.89 0.52 0.51 2.16Goethite FeO(OH) 4.28 7.34 7.01 4.49 3.17 3.16 0.22

Grossular Ca3Al2Si3O12 3.65 2.22 2.12 4.45 1.19 1.18 0.77Hematite Fe2O3 5.26 9.89 9.45 4.48 4.21 4.20 0.16Ilmenite FeTiO3 4.76 7.26 6.95 4.34 3.17 3.13 1.05Kaolinite Al2Si2O5(OH)4 2.60 0.91 0.87 4.90 0.60 0.59 1.95

K-feldspar KAlSi3O8 2.56 1.22 1.16 4.65 0.71 0.71 0.00Lepidolite KLi2AlSi4O10(OH)2 2.83 1.21 1.16 4.45 0.74 0.73 1.35Magnetite Fe3O4 5.18 10.03 9.58 4.48 4.25 4.25 0.14

Molybdenite MoS2 5.00 29.65 30.50 2.79 12.03 12.50 3.76Olivine Fe2SiO4 3.32 5.20 4.97 4.42 2.27 2.26 0.44

Pecoraite Ni3S2O5(OH4) 3.47 6.65 6.92 3.87 2.57 2.70 4.81Pyrite FeS2 5.01 8.02 7.81 2.52 3.48 3.50 0.63

Pyrope Mg3Al2Si3O12 3.75 1.34 1.28 4.51 0.87 0.86 1.30Quartz SiO2 2.65 1.01 0.96 4.95 0.64 0.63 1.68

Rynersonite CaTa2O6 6.39 35.64 36.00 0.99 15.13 15.20 0.46Safflorite CoAs2 7.47 32.11 31.10 3.13 12.91 13.40 3.66Siderite FeCO3 3.96 5.41 5.17 4.47 2.41 2.40 0.35

Spessartine Mn3Al2Si3O12 4.29 4.22 4.33 2.51 2.00 1.98 0.94Sphalerite ZnS 4.10 11.68 11.90 1.82 4.78 4.80 0.42

Talc Mg3Si4O10(OH)2 2.75 0.99 0.94 4.85 0.64 0.64 0.00Uvarovite Ca3Cr2Si3O12 3.85 3.55 3.55 0.15 1.70 1.69 0.69

Wolframite FeWO4 7.30 38.12 38.70 1.50 16.16 16.30 0.86Zircon ZrSiO4 4.71 20.06 21.10 4.94 8.26 8.40 1.67

Evaluating the required linear attenuation coefficient difference to determine discriminationbetween minerals is not trivial. This is due to grey value overlap between minerals which cannotbe avoided in most cases, when using XCT. Partly this is because most naturally occurring mineralshave inclusions of other minerals in them to some extent. This is well demonstrated by the quartzand kaolinite samples used here. The calculated linear attenuation coefficient difference betweenthese minerals is 9.42%. However, the measured grey value difference between these two mineralswas determined to be 4.31%, resulting in only partial discrimination (Figure 6D,E). The grey valueoverlap is due to the presence of small inclusions of quartz and k-feldspar in the kaolinite (Figure 7).Figure 6 is given at such a resolution that the small inclusions cannot be seen but the QEMSCANanalysis supports their presence. A similar situation exists between goethite and chromite (Figure 6J,K)where the linear attenuation coefficient difference is higher (12.99%) but the grey value difference islower (7.1%), resulting in only partial discrimination of the two minerals. In this case, the grey valueoverlap is due to different Fe-concentrations within the goethite matrix. In some cases, the presenceof mineral inclusions does not affect the mineral discrimination but still affects the mean grey valuethat is supposed to represent the true linear attenuation coefficient. This is a case with almandine,which has a higher linear attenuation coefficient than andradite, but has a lower mean grey value(Table 3 and Figure 7) due to the presence of uniformly distributed pyrope and minor grossular as

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inclusions. Despite the presence of these mineral inclusions in almandine, almandine was clearlydiscriminated from andradite with a grey value difference of 18.76% and a linear attenuation coefficientdifference of 14.22% (Table 4 and Figure 6). Similarly, apatite and fluorite (Figure 6H,I) are completelydiscriminated from one another in terms of their grey value levels (9.26%) but have a lower linearattenuation coefficient difference (6.06%). This is attributed to the fact that there are no inclusionswithin the minerals. This shows that a minimum linear attenuation coefficient difference of 6% isenough to discriminate between minerals. Minerals with linear attenuation coefficient difference lessthan this may be difficult to discriminate. Hematite and magnetite have a linear attenuation coefficientdifference of 1.42% with a density difference of 1.54%, resulting in a grey value difference of 4.27%.Therefore, hematite and magnetite cannot be discriminated from each other according to Figure 6.Thus, it would seem that minerals with a linear attenuation coefficient difference of less than ~4.3%cannot be differentiated using XCT, whereas minerals with a linear attenuation coefficient differenceabove ~6% can be differentiated. However, this assumes that the target material is tungsten, mineralsare pure and free of inclusions. If the minerals are not compositionally pure then the presence ofinclusions complicates discrimination as in the case of the quartz and kaolinite samples used here.In addition to this, different target materials (e.g., Silver, Copper, Molybdenum) would have differenteffective energies at the same X-ray voltage but the minimum required attenuation coefficient differenceis expected to remain the same. This means that the X-ray voltage for each target material wouldbe different in order to achieve the same minimum required attenuation coefficient difference todifferentiate minerals.

Table 3. Grey value variation of different minerals with their corresponding density (https://www.mindat.org/) and linear attenuation coefficients at 45.5 keV effective energy.

Mineral Chemical Formula Density g/cm3 Attenuation Coefficient cm−1 Mean Grey Value

Almandine Fe3Al2Si3O12 4.32 4.36 28,084.5Andradite Ca3Fe3+

2Si3O12 3.86 3.74 34,569.4Grossular Ca3Al2Si3O12 3.65 2.05 22,971.9

Quartz SiO2 2.65 0.93 10,540.6Kaolinite Al2Si2O5(OH)4 2.60 0.85 11,014.9Dolomite CaMg(CO3)2 2.85 1.29 15,047.8

Calcite CaCO3 2.71 1.66 18,285.0Fluorite CaF2 3.13 2.31 23,956.0Apatite Ca5(PO4)3OH 3.15 2.15 21,737.9Goethite FeO(OH) 4.28 6.70 36,097.6Chromite FeCr2O4 4.79 7.70 38,856.9Magnetite Fe3O4 5.18 9.15 54,895.8Hematite Fe2O3 5.26 9.02 57,344.8

Minerals 2020, 10, x FOR PEER REVIEW 11 of 16

same. This means that the X-ray voltage for each target material would be different in order to achieve the same minimum required attenuation coefficient difference to differentiate minerals.

Table 3. Grey value variation of different minerals with their corresponding density (https://www.mindat.org/) and linear attenuation coefficients at 45.5 keV effective energy.

Mineral Chemical Formula Density g/cm3 Attenuation Coefficient cm−1 Mean Grey Value Almandine Fe3Al2Si3O12 4.32 4.36 28084.5 Andradite Ca3Fe3+2Si3O12 3.86 3.74 34569.4 Grossular Ca3Al2Si3O12 3.65 2.05 22971.9

Quartz SiO2 2.65 0.93 10540.6 Kaolinite Al2Si2O5(OH)4 2.60 0.85 11014.9 Dolomite CaMg(CO3)2 2.85 1.29 15047.8

Calcite CaCO3 2.71 1.66 18285.0 Fluorite CaF2 3.13 2.31 23956.0 Apatite Ca5(PO4)3OH 3.15 2.15 21737.9 Goethite FeO(OH) 4.28 6.70 36097.6 Chromite FeCr2O4 4.79 7.70 38856.9 Magnetite Fe3O4 5.18 9.15 54895.8 Hematite Fe2O3 5.26 9.02 57344.8

Figure 7. Mineral classification using QEMSCAN in order to understand the discrimination between the minerals: (A) almandine, (B) andradite, (C) grossular, (D) quartz, (E) kaolinite, (F) dolomite, (G) calcite, (H) apatite, (I) fluorite, (J) goethite, (K) chromite, (L) magnetite and (M) hematite. False colour image (refer also to Figure 6).

Table 4. Mineral discrimination using linear attenuation coefficient difference at 45.5 keV effective energy in conjunction with grey value and density difference. BH = beam hardening.

Mineral Comparison

Filter Material/BH Correction

Factor

% Grey Value

Difference

% Attenuation Coefficient Difference

% Density Difference Discrimination

Almandine vs. Andradite

0.25mm Cu/2

18.8 14.2 10.7 Yes

Almandine vs. Grossular

18.2 53.0 15.5 Yes

Grossular vs. Andradite 33.6 45.2 5.44 Yes Quartz vs. Kaolinite

No Filter/2

4.31 9.42 1.89 Partial Quartz vs. Dolomite 30.0 27.6 7.02 Yes

Quartz vs. Calcite 42.4 43.7 2.21 Yes Kaolinite vs. Dolomite 26.8 34.4 8.77 Yes

Kaolinite vs. Calcite 39.8 49.0 4.06 Yes Dolomite vs. Calcite 17.7 22.3 4.91 Yes Fluorite vs. Apatite 0.25mm Cu/1 9.26 6.06 0.63 Yes

Goethite vs. Chromite 0.25mm Cu/2 7.10 13.0 10.7 Partial

Figure 7. Mineral classification using QEMSCAN in order to understand the discrimination betweenthe minerals: (A) almandine, (B) andradite, (C) grossular, (D) quartz, (E) kaolinite, (F) dolomite,(G) calcite, (H) apatite, (I) fluorite, (J) goethite, (K) chromite, (L) magnetite and (M) hematite. Falsecolour image (refer also to Figure 6).

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Table 4. Mineral discrimination using linear attenuation coefficient difference at 45.5 keV effectiveenergy in conjunction with grey value and density difference. BH = beam hardening.

Mineral Comparison

FilterMaterial/BHCorrection

Factor

% Grey ValueDifference

% AttenuationCoefficientDifference

% DensityDifference Discrimination

Almandine vs. Andradite0.25 mm Cu/2

18.8 14.2 10.7 YesAlmandine vs. Grossular 18.2 53.0 15.5 YesGrossular vs. Andradite 33.6 45.2 5.44 Yes

Quartz vs. Kaolinite

No Filter/2

4.31 9.42 1.89 PartialQuartz vs. Dolomite 30.0 27.6 7.02 Yes

Quartz vs. Calcite 42.4 43.7 2.21 YesKaolinite vs. Dolomite 26.8 34.4 8.77 Yes

Kaolinite vs. Calcite 39.8 49.0 4.06 YesDolomite vs. Calcite 17.7 22.3 4.91 Yes

Fluorite vs. Apatite 0.25 mm Cu/1 9.26 6.06 0.63 Yes

Goethite vs. Chromite 0.25 mm Cu/2 7.10 13.0 10.7 Partial

Gothite vs. Magnetite

1 mm Cu +1 mm Al/3

34.2 26.8 17.4 YesGoethite vs. Hematite 37.1 25.7 18.6 Yes

Chromite vs. Magnetite 29.2 15.9 7.53 YesChromite vs. Hematite 32.2 14.6 8.94 YesMagnetite vs. Hematite 4.27 1.42 1.52 No

4. Discussion

The linear attenuation coefficient database developed above is a practical, user friendly tool forcalculating linear attenuation coefficients. It is also very flexible in that it allows the user to calculateattenuation coefficients at any effective X-ray energy between 41.7 keV and 74.6 keV and this canbe done offline. Comparison of the MXLAC database with that of the NIST online calculation toolindicates that the difference between the two is less than 5%. MXLAC highlights the importance ofknowing the exact mineral composition (in terms of specific cation and anion numbers) and density inorder to predict which minerals can be discriminated and which cannot. In the following discussion,several examples of where MXLAC can be used to better set up XCT experiments are demonstrated.

4.1. Mineral Composition and Linear Attenuation Coefficient

For minerals with no solid solution, such as quartz, the calculation of the linear attenuationcoefficient is straight forward as the chemical formula is fixed. In the case of quartz, which is SiO2,the linear attenuation coefficient is 0.93 cm−1 at 45.5 keV. However, for minerals with solid solutionsubstitution, it is necessary to know the exact composition of the mineral in the sample being analysed.Garnet which is a common mineral in a variety of rocks elegantly illustrates this. The generic formulafor garnet is X3Y2(SiO4)3 with X representing Mg, Fe, Mn or Ca and Y representing Al or Cr [28].The example shown in Figure 4 is of a pyrope garnet, with the composition Mg3Al2Si3O12 anddensity 3.75 g/cm3 and has the linear attenuation coefficient of 1.25 cm−1 at 45.5 keV effective energy.This is distinct from garnet with different compositions such as almandine Fe3Al2Si3O12 (4.32 g/cm3,4.36 cm−1), spessartine Mn3Al2Si3O12 (4.29 g/cm3, 4.16 cm−1), andradite Ca3Fe3+

2Si3O12 (3.86 g/cm3,3.74 cm−1), uvarovite Ca3Cr2Si3O12 (3.85 g/cm3, 3.41 cm−1), and grossular Ca3Al2Si3O12 (3.65 g/cm3,2.05cm−1) calculated at the same X-ray energy. The difference in the linear attenuation coefficientsis a result of differences in the densities and chemical compositions of these minerals even thoughthe structural formula remains constant and the physical properties of all the garnet varieties remainsvery similar. As a consequence of the differences in linear attenuation coefficient, these minerals willappear differently on a 2D image slice except for almandine and spessartine due to a lower attenuationcoefficient difference of 4.6%.

The example given above assumes that garnet exists as one of the end-member compositions, butthis is not usually the case, with garnet exhibiting solid solution substitution within both the X and Ycation sites. What this means in practice is that garnet in any given rock will have a linear attenuation

Minerals 2020, 10, 441 12 of 15

coefficient of between 4.36 cm−1 and 1.25 cm−1 at 45.5 keV depending on its exact composition.For example, a garnet that is dominantly Fe-rich but also containing appreciable amounts of Mg aswell as minor amounts of Mn and Ca in the cation proportions (Fe2.1Mg0.7Mn0.15Ca0.05)Al2Si3O12

would have an approximate composite density of 4.16 g/cm3 and a linear attenuation coefficient of3.60 cm−1 at 45.5 keV. This is significantly different from the linear attenuation coefficient valuesfor either end-member almandine or pyrope. Assuming a linear attenuation coefficient of either ofthese end-members would result in significant error associated with the differentiation of this garnetcomposition from other minerals with linear attenuation coefficients in this range at 45.5 keV. Similarly,using the density of one garnet composition, when in fact a different composition is present, will alsoresult in the calculation of an incorrect linear attenuation coefficient.

4.2. Mineral Density and Attenuation

MXLAC can also be used to illustrate the importance of upfront mineral density and compositionalinformation when differentiating minerals using XCT. To evaluate this issue, iron ore is consideredwhere iron ore mineralisation involves both iron ore minerals themselves (hematite, magnetite andgoethite) as well as commonly associated gangue minerals may be present (quartz, kaolinite, gibbsite,chlorite, siderite, ankerite, fluorite, barite and apatite). The theoretically calculated linear attenuationcoefficients for these minerals (Table 5) were compared in order to evaluate the impact of differentdensities on the attenuation coefficient. This is well illustrated by barite (BaSO4), which has a lowerdensity (4.48 g/cm3) than hematite and magnetite (5.26 and 5.18 g/cm3) respectively. These mineralshave a minimum density difference 13.51% which suggest that barite should appear darker or withlower grey values than hematite and magnetite. However, this is not the case, because barite has ahigher linear attenuation coefficient of 46.1 cm−1 at 45.5 keV effective X-ray energy which would makeit to appear brighter. In contrast, magnetite has a linear attenuation coefficient of 9.15 cm−1 whilehematite is 9.02 cm−1. The linear attenuation coefficients of hematite and magnetite are similar becausetheir densities and chemical composition are similar, Table 5. In addition to this the majority of theminerals with a density difference <5% presented in Table 4 were partially or full distinguishable fromeach other. This emphasizes the need to use linear attenuation coefficient information to predict ifminerals can be discriminated or not as compared to using the density information alone.

Table 5. Summary of common minerals in iron ores, alongside their formulae and density https://www.mindat.org/.

Iron Mineral Formula Density g/cm3 Gangue Mineral Formula Density g/cm3

Hematite Fe2O3 5.26 Quartz SiO2 2.65Magnetite Fe3O4 5.18 Kaolinite Al2Si2O5(OH)4 2.60Goethite FeO(OH) 4.28 Fluorite CaF2 3.13Siderite FeCO3 3.96 Barite BaSO4 4.48Chlorite (Mg)5Al2Si3O10(OH)8 3.20 Apatite Ca5(PO4)3OH 3.19Pyrite FeS2 5.01 Gibbsite Al(OH)3 2.34

Ilmenite FeTiO3 4.76 Ankerite CaFe(CO3)2 3.20

4.3. Influence of Mineral Composition vs. Density on Attenuation Coefficient

Linear attenuation coefficients are much more strongly impacted by mineral composition than theyare by density. This would suggest that it is much more important to obtain an accurate composition inorder to optimize the discrimination between the minerals than it is to obtain an accurate density. This isillustrated using the example of olivine, which has a general structural formula of (Mg,Fe)2SiO4, and anaverage density of 3.3 g/cm3. Olivine of this composition and density, has a linear attenuation coefficientof 4.20 cm−1 at an arbitrary effective energy of 41.7 keV, which is distinct from olivine of compositionMg1.6Fe0.4SiO4 with an attenuation coefficient of 2.6 cm−1 at the same energy and density. Swappingthe ratio of magnesium and iron (i.e., Mg0.4Fe1.6SiO4) results in an attenuation coefficient of 5.49 cm−1,yielding an attenuation coefficient difference of 52.64% from the Mg1.6Fe0.4SiO4 composition when thesame density is used for the calculations. When the same scenario is considered for Mg0.4Fe1.6SiO4

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with a density reduction of 52.64% to 1.74 g/cm−3 from its average density of 3.3 g/cm3, its attenuationcoefficient is 2.9 cm−1 which is 35.41% less than when the density is 3.3 g/cm3. This means that a52.64% reduction in density only resulted in a 32.42% reduction in attenuation coefficient for thesame composition. Similarly, andradite and uvarovite garnets have almost identical densities (3.86 vs.3.85 g/cm−1) but linear attenuation coefficients of 4.88 and 4.31 cm−1 with a percentage attenuationcoefficient difference of 11.68% at 41.7 keV. Using density information alone would suggest that thesetwo minerals cannot be discriminated even though their linear attenuation coefficients suggest thatthey can be. Thus, a change in composition has more effect on the attenuation coefficient than a changein density and hence knowing the exact composition of the minerals to be interrogated with XCT iscritical to evaluate whether XCT is an appropriate tool to use.

5. Conclusions

Theoretically calculated linear attenuation coefficients form an important basis for planning XCTscans with optimal image contrast. These attenuation coefficients can be utilised to optimise the X-rayscanning energy to discriminate minerals according to exact mineral compositions as well as densityfor proper quantification. The data bank presented here is designed not only to be user friendly andcompare attenuation coefficient information of two different minerals at the same time but also to beeasily available. The discrimination between minerals with an attenuation coefficient difference of lessthan 6% will be challenging. This will depend on the complexity of the minerals especially if they haveinclusions as observed between quartz and kaolinite with grey values difference of 4.31% even thoughtheir attenuation coefficient difference is >9%. Optimal discrimination using attenuation coefficientsdepends more on the composition but also on scanning parameters including appropriate filter materialbeing used. Different minerals respond differently on the type of filter material being used, especiallythose with a density greater than 3 g/cm3. Minerals with a density less than 3 g/cm3 might not requireany application of filter materials in order to optimize discrimination. This depends on the samplesize and complexity of the sample being scanned (mineral inclusion). This means that minerals ofinterest should be well defined and understood prior to scanning so that the limitations associated withdiscriminating minerals using linear attenuation coefficients can be evaluated before XCT scanning.However, the extent of mineral inclusions that affects discrimination and direct comparison betweenlinear attenuation coefficient difference with grey value difference should be investigated in more detailin future studies. This will include studying how uniform and non-uniform distribution of mineralinclusions affects grey value difference that is supposed to correlate directly with the attenuationcoefficient difference. In addition to this different detector filter materials that can minimise the impactof environmental scatter that contribute to inaccurate mineral grey values should also be investigatedin order to obtain the expected grey value difference that correlates with the attenuation coefficientdifference. This will allow effective utilization or application of the XCT technique to the geologicalsamples. The effective application of the XCT techniques together with the MXLAC spreadsheet is notonly important for geological samples but also to any research field that studies attenuating materialsof any kind, e.g., material sciences, electrochemical studies, etc. Most importantly understandingthe limitations of XCT will lead to further refinements of the XCT technique that may in the futureovercome these limitations.

Supplementary Materials: The following are available online at http://www.mdpi.com/2075-163X/10/5/441/s1,The MXLAC spreadsheet to calculate the linear attenuation coefficient with a title ‘MXLAC—A tool to calculatelinear attenuation coefficient’ is included.

Author Contributions: L.C.B.: Conceptualization, analysis, methodology and writing—original draft. J.A.M.:Methodology, supervision and writing—review & editing. M.B.: Methodology, supervision and writing—review& editing. All authors have read and agreed to the published version of the manuscript.

Funding: The authors would like to thank Necsa (Nuclear Energy Corporation of South Africa) and themanagement team for funding and access to the Microfocus system in the MIXRAD Lab, which is a DST-NRF(Department of Science and Technology—National Research Funding) funded facility through the NEP-RISP(National Equipment Programme—Research Infrastructure Support Programmes) program. The project is

Minerals 2020, 10, 441 14 of 15

supported through SAMMRI (South African Minerals to Metals Research Institute), grant number: S1511. Thisproject is also based on the research supported in part by the National Research Foundation of South Africa(Grant Numbers 86054, 99005). Any opinions, findings and conclusions or recommendations expressed in anypublication generated by the NRF supported research is that of the author(s), and that the NRF accepts no liabilitywhatsoever in this regard.

Acknowledgments: The authors would like to thank Andrew Watson for assistance with compiling the diagrams,Madelaine Frazenburg for SEM-EDS analysis at SU and Gaynor Yorath and the UCT QEMSCAN team for assistancewith QEMSCAN analysis.

Conflicts of Interest: The authors declare no conflict of interest.

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